Existence of functions of fixed trace and minimum weighted total variation

Abstract

For Ωa C^{2}-smooth domain, and a positive bounded continuous map a \in C(Ω), we prove existence of a minimizer of the functional u \mapsto $\int_Ω a|Du| over the space BV(Ω) of functions of bounded variation with fixed trace f \in L^{1}(\partialΩ). The method of proof is constructive.

this paper has been withdrawn by the author due to a crucial error